Artículo
Abstract:
In this paper, we establish global Sobolev a priori estimates for Lp-viscosity solutions of fully nonlinear elliptic equations as follows: F(D2u,Du,u,x) = f(x)in Ωu(x) = φ(x) on ∂Ω by considering minimal integrability condition on the data, i.e. f Lp(Ω),φ W2,p(Ω) for n < p < ∞ and a regular domain Ω ⊂ Rn, and relaxed structural assumptions (weaker than convexity) on the governing operator. Our approach makes use of techniques from geometric tangential analysis, which consists in transporting "fine" regularity estimates from a limiting operator, the Recession profile, associated to F to the original operator via compactness methods. We devote special attention to the borderline case, i.e. when f p -BMO ⊇ L∞. In such a scenery, we show that solutions admit BMO type estimates for their second derivatives. © 2018 World Scientific Publishing Company.
Registro:
| Documento: | Artículo |
| Título: | An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates |
| Autor: | Da Silva, J.V.; Ricarte, G.C. |
| Filiación: | FCEyN, Department of Mathematics, Universidad de Buenos Aires, Ciudad Universitaria-Pabellón I- (C1428EGA), Buenos Aires, Argentina Department of Mathematics, Universidade Federal Ceará, Fortaleza, CE-60455-760, Brazil |
| Palabras clave: | fully nonlinear elliptic equations; Global W 2, p and BMO type estimates; relaxed convexity assumptions |
| Año: | 2018 |
| DOI: | http://dx.doi.org/10.1142/S0219199718500530 |
| Título revista: | Communications in Contemporary Mathematics |
| Título revista abreviado: | Commun. Contemp. Math. |
| ISSN: | 02191997 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v_n_p_DaSilva |
Citas:
---------- APA ----------
Da Silva, J.V. & Ricarte, G.C. (2018) . An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates. Communications in Contemporary Mathematics.http://dx.doi.org/10.1142/S0219199718500530
---------- CHICAGO ----------
Da Silva, J.V., Ricarte, G.C. "An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates" . Communications in Contemporary Mathematics (2018).http://dx.doi.org/10.1142/S0219199718500530
---------- MLA ----------
Da Silva, J.V., Ricarte, G.C. "An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates" . Communications in Contemporary Mathematics, 2018.http://dx.doi.org/10.1142/S0219199718500530
---------- VANCOUVER ----------
Da Silva, J.V., Ricarte, G.C. An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates. Commun. Contemp. Math. 2018.http://dx.doi.org/10.1142/S0219199718500530
